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Mathematical Biology

  • Textbook
  • © 1993

Overview

Authors:
  1. James D. Murray

    1. Applied Mathematics FS-20, University of Washington, Seattle, USA

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Part of the book series: Biomathematics (BIOMATHEMATICS, volume 19)

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Table of contents (20 chapters)

  1. Front Matter

    Pages I-XIV
    Download chapter PDF

  2. Continuous Population Models for Single Species

    • James D. Murray
    Pages 1-35

  3. Discrete Population Models for a Single Species

    • James D. Murray
    Pages 36-62

  4. Continuous Models for Interacting Populations

    • James D. Murray
    Pages 63-94

  5. Discrete Growth Models for Interacting Populations

    • James D. Murray
    Pages 95-108

  6. Reaction Kinetics

    • James D. Murray
    Pages 109-139

  7. Biological Oscillators and Switches

    • James D. Murray
    Pages 140-178

  8. Belousov-Zhabotinskii Reaction

    • James D. Murray
    Pages 179-199

  9. Perturbed and Coupled Oscillators and Black Holes

    • James D. Murray
    Pages 200-231

  10. Reaction Diffusion, Chemotaxis and Non-local Mechanisms

    • James D. Murray
    Pages 232-253

  11. Oscillator Generated Wave Phenomena and Central Pattern Generators

    • James D. Murray
    Pages 254-273

  12. Biological Waves: Single Species Models

    • James D. Murray
    Pages 274-310

  13. Biological Waves: Multi-Species Reaction Diffusion Models

    • James D. Murray
    Pages 311-359

  14. Travelling Waves in Reaction Diffusion Systems with Weak Diffusion: Analytical Techniques and Results

    • James D. Murray
    Pages 360-371

  15. Spatial Pattern Formation with Reaction/Population Interaction Diffusion Mechanisms

    • James D. Murray
    Pages 372-434

  16. Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms

    • James D. Murray
    Pages 435-480

  17. Neural Models of Pattern Formation

    • James D. Murray
    Pages 481-524

  18. Mechanical Models for Generating Pattern and Form in Development

    • James D. Murray
    Pages 525-592

  19. Evolution and Developmental Programmes

    • James D. Murray
    Pages 593-609

  20. Epidemic Models and the Dynamics of Infectious Diseases

    • James D. Murray
    Pages 610-650
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Keywords

About this book

Mathematics has always benefited from its involvement with developing sciences. Each successive interaction revitalises and enhances the field. Biomedical science is clearly the premier science of the foreseeable future. For the continuing health of their subject mathematicians must become involved with biology. With the example of how mathematics has benefited from and influenced physics, it is clear that if mathematicians do not become involved in the biosciences they will simply not be a part of what are likely to be the most important and exciting scientific discoveries of all time. Mathematical biology is a fast growing, well recognised, albeit not clearly defined, subject and is, to my mind, the most exciting modern application of mathematics. The increasing use of mathematics in biology is inevitable as biol­ ogy becomes more quantitative. The complexity of the biological sciences makes interdisciplinary involvement essential. For the mathematician, biology opens up new and exciting branches while for the biologist mathematical modelling offers another research tool commmensurate with a new powerful laboratory technique but only if used appropriately and its limitations recognised. However, the use of esoteric mathematics arrogantly applied to biological problems by mathemati­ cians who know little about the real biology, together with unsubstantiated claims as to how important such theories are, does little to promote the interdisciplinary involvement which is so essential. Mathematical biology research, to be useful and interesting, must be relevant biologically.

Authors and Affiliations

  • Applied Mathematics FS-20, University of Washington, Seattle, USA

    James D. Murray

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